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Derivative 1/x³

  1. Sep 26, 2011 #1
    how to compute the ANTI derivative of 1 / x^3
    I think I need the formula: f(x) = 1/x^n than f'(x) = -n/x^n+1 but I'm not sure and don't know how to use it.

    I know the answer is: -0.5 * x^-2 but have no idea why.

    could someone explain this to me please?
     
  2. jcsd
  3. Sep 26, 2011 #2

    LCKurtz

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    The familiar antiderivative formula

    [tex]\int x^n\, dx = \frac{x^{n+1}}{n+1}+C[/tex]

    also works for negative exponents. Write your fraction as a negative exponent.
     
  4. Sep 26, 2011 #3
    thanks for your answer.

    now how would I put 1/x³ into that formula to get -0.5 * x^-2 ?
     
  5. Sep 26, 2011 #4

    LCKurtz

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    Write 1/x³ as xn using a negative exponent and use the formua.
     
  6. Sep 26, 2011 #5
    hm okay. like x^-3. got it.

    I guess I should learn this formula, not only because it's a "familiar" one for you guys. But also because for some reason it's not on my formula sheet.

    :) tnx for your help.
     
  7. Sep 26, 2011 #6

    SteamKing

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